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Mayan Mathematics and Numbers  Symbols of Their Culture
Mayan Math Is Not That Hard
My fascination with the ancient Mayan culture has finally led me to a math lesson. While I readily admit that math wasn’t my favorite subject in school, I definitely can appreciate the Mayan approach to math. They were quite advanced for their time.
This hub explores the more simple aspect of Mayan math: how they wrote their numbers and how their numbers related to their concept of time.
© C. Calhoun 2012. All rights reserved.
Where the Mayans Lived  Present Day Central America, Including the Yucatan Peninsula
The Concept of Zero
By the end of the third century, the Mayans had already figured how to use the number zero. They used a shell to represent it. They figured that though it didn’t presently have “matter,” it could actually have matter at some future point in time.
Interestingly, the Mayans had the number zero figured out ahead of many other civilizations.
Books and References
The Mayan Numeral System Was Directly Tied to Their Calendar and to the Concept of Time
The Mayan calendar told them when to plant crops, marked the changing seasons, and even when to celebrate their religious rites.
Because of the Mayans’ ability to use the number zero and write just about any number they could imagine, they could use their calendar to predict events thousands of years into the future.
The calendar was made of two wheels. They meshed together to make a 365day year.
The year looked different than our present method of keeping track of days, months and years. Their calendar was 18 months long, with each month containing 20 days each. The Mayans considered the 5 days at the end of the year to be bad luck.
The Mayan notion of a day was that each day had a certain amount of “contents.” At the end of the day, when empty, another day would arrive, ready with its own contents.
The Mayan concept of time wasn’t linear, either. To them, it was cyclical. Because of their use of the wheel, they expected events to repeat themselves in the future.
For a particular day to repeat itself, though, 52 years had to pass. The Calendar Wheel was a cycle of 52 years. It is noteworthy, though, that for the Mayans, time neither had a beginning nor an end.
The Mayan Math System Used a Base 20 Approach
Remember how the Mayan calendar had 20 days in each month? That’s a reflection of their way of doing numbers.
In the United States and in many other industrialized societies, the decimal system is the mathematical approach of these cultures. The root deci means “ten.” It is a system that uses base 10.
The Mayans, however, used a base 20 form of mathematics.
Their mathematical symbols comprised of three characters: a shell, dots and bars.
The shell = 0.
The dot = 1.
The bar = 5.
Thus, the numbers 119 were made of the shell, dots and numbers. (See photo.)
The number 36 could be written as a power of 20: 1 x 20 = 20 and 20 + 16 = 36. If you compare that to the decimal system, it looks different: 3 x 10 = 30 and 30 + 6 = 36.
Here’s where it gets a little more complicated. Since the Mayan system was base 20, things changed after number 19: they moved to the next place value.
Another interesting point is that the Mayans wrote their place values vertically. The smallest number went on the bottom, and progressively higher numbers went on top, based on powers of 20. (see table)
The 1s place was at the bottom, then the 20s (20 x 1) place above that, then the 400s place (20 x 20), followed by the 8000s (20 x 20 x 20), then the 160,000 (20 x 20 x 20 x 20), and so on.
Thus, if you wanted to write the number 35 (see examples in red below), you would use all 19 numbers in the ones place, and a "twenty" in the 20s place.
Mayan Numbers 85, 37 and 92 Written Out
The Number 18,425 in Mayan Numbers
Power of 20
 Total Power
 In Words
 Mayan Number
 Actual Number


20 x 20 x 20 x 20
 160,000
 
 
 

20 x 20 x 20
 8,000
 2 eight thousands
 ••
 16,000

20 x 20
 400
 6 four hundreds
 _•
 2.400

20 x 1
 20
 1 twenty
 •
 20

1 x 0
 1
 5 ones
 
 5

18,425

Comments
Most math is way over my head, but since the Mayans built their systems by studying astronomy, I occasionally get a glimpse into their math. The more you study their rich culture and building construction, the more fascinating the Mayans become.
They are a very unique group!
I loved the Mayan math lesson! Having used the system of tens all my life, it was easy to believe this was the only math system. Thanks for a fresh look at very ancient mathematics. Your presentation was so simple and logical that it was easy to grasp the basic concepts. Fun read, voted up, useful and interesting!
Agreed! I think they had very developed mathematics knowledge than us.
Cyndi  What a well researched and interesting hub. I knew nothing at all about the Mayans so this has been a brand new learning experience for me (my favourite kind :o)
My goodness, girl! You might just have another HOTD with this one. You really did a lot of research on this, and it was worth it. I love your drawings, too.
I voted it up, etc. and will share.
I just noticed on your profile, you don't mention your HOTD about the OWL. Mary
Interesting hub. My question is, though unrelated with Mayan mathematics but related to Mayans is: Were Mayans a part of the people migrated from eastern end of Russia to Alaska and then to Canada, US and further south? Or they were original inhabitants of America?
What a great topic for a hub. I admit I didn't know much about Mayan Mathematics until I read your fascinating hub. Voted up, useful, interesting, and shared! Take care, Kelley
Very interesting Hub. Thank you for sharing this information. As a Math teacher I of course had worked with different number bases, but had not connected it to the Mayas. Voted up, awesome and interesting! Have a good day and be happy!
I'm trying to cite this page. Can i have your name and the year you wrote it?
Lame, who cares about old math? Math is stupid NOW, it was lamer a long time ago too.
Interesting. I had not know that the Mayans had perfected Zero first.
Love it! Fascinating and wellwritten. What a cool research idea. Voted up and beautiful.
Great job, CC. I didn't know about the math in this depth that the Mayans were responsible for.
This is a great resource, Cyndi! Thanks!
I love that you mentioned that the Mayan calendar has no beginning and no end. This is correct. Calendars are just a man made measure of what we call 'time'.
Interesting read. I know a bit about nonbaseten systems (e.g. hexidecimal), but it's fascinating how they wrote their numbers out.
Also didn't know their calendar worked that way. I'm working on a fantasy novel in which the fictional world uses twelve 30day months with a "yearend" period for the extra days. All this time I thought I was being original!
I'm not a big math buff either but tying the subject to this civilization makes it interesting. They obviously used all their fingers and toes to come up with the base 20 system while Western civilization just based it on the fingers. One thing I'd like to point out is that the Maya are very much alive and well and still living in the Yucatan peninsula. In fact, one of my friends was of Mayan ancestry, though he was born in this country. When he returned from his first trip to the Yucatan, he remarked that all the locals there and in the ancient wall paintings looked like him! Your hub is, of course, referring to the ancient Maya, who are ancestors of the modern ones. Voting this Up and Interesting.
Interesting and informative. A view into the Mayan way of calculations presented very well. Great hub, voted up.
This was fascinating and very educational. They really were an advanced civilization in many areas. Great coverage of this concept.
Interesting stuff! I had no idea they used a base 20 system. Thank you for a great hub!
Incredibly informative hub! I learned a ton about Mayan Math. You made it very simple to grasp, and the images you provide are fantastic. Nice article! A very fun read.
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